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Higher-order Lindley equations

Author

Listed:
  • Karpelevich, F. I.
  • Kelbert, M. Ya.
  • Suhov, Yu. M.

Abstract

A model of a queueing network is proposed which leads to a stochastic equation generalizing a standard Lindley equation for a single FCFS server. We study the problem of the existence and uniqueness of a stationary solution to this equation and its connection with random processes on a Cayley tree.

Suggested Citation

  • Karpelevich, F. I. & Kelbert, M. Ya. & Suhov, Yu. M., 1994. "Higher-order Lindley equations," Stochastic Processes and their Applications, Elsevier, vol. 53(1), pages 65-96, September.
    • Handle: RePEc:eee:spapps:v:53:y:1994:i:1:p:65-96
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    Citations

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    Cited by:

    1. Biggins, J. D., 1998. "Lindley-type equations in the branching random walk," Stochastic Processes and their Applications, Elsevier, vol. 75(1), pages 105-133, June.
    2. Mariana Olvera-Cravioto & Octavio Ruiz-Lacedelli, 2021. "Stationary Waiting Time in Parallel Queues with Synchronization," Mathematics of Operations Research, INFORMS, vol. 46(1), pages 1-27, February.
    3. Jelenković, Predrag R. & Olvera-Cravioto, Mariana, 2015. "Maximums on trees," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 217-232.
    4. Onno Boxma & Andreas Löpker & Michel Mandjes & Zbigniew Palmowski, 2021. "A multiplicative version of the Lindley recursion," Queueing Systems: Theory and Applications, Springer, vol. 98(3), pages 225-245, August.
    5. Fraiman, Nicolas & Lin, Tzu-Chi & Olvera-Cravioto, Mariana, 2023. "Stochastic recursions on directed random graphs," Stochastic Processes and their Applications, Elsevier, vol. 166(C).
    6. Basrak, Bojan & Conroy, Michael & Olvera-Cravioto, Mariana & Palmowski, Zbigniew, 2022. "Importance sampling for maxima on trees," Stochastic Processes and their Applications, Elsevier, vol. 148(C), pages 139-179.

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